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Nonconforming events are rare in high-quality processes, and the time between events (TBE) may follow a skewed distribution, such as the gamma distribution. This study proposes one- and two-sided triple homogeneously weighted moving average charts for monitoring TBE data modeled by the gamma distribution. These charts are labeled as the THWMA TBE charts. Monte Carlo simulations are performed to approximate the run length distribution of the one- and two-sided THWMA TBE charts. The THWMA TBE charts are compared to competing charts like the DHWMA TBE, HWMA TBE, THWMA TBE, DEWMA TBE, and EWMA TBE charts at a single shift and over a range of shifts. For the single shift comparison, the average run length (ARL) and standard deviation run length (SDRL) measures are used, whereas the extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are employed for a range of shifts comparison. The comparison reveals that the THWMA TBE charts outperform the competing charts at a single shift as well as at a certain range of shifts. Finally, two real-life data applications are presented to evaluate the applicability of the THWMA TBE charts in practical situations, one with boring machine failure data and the other with hospital stay time for traumatic brain injury patients. [ABSTRACT FROM AUTHOR]

Nonconforming events rarely occur in high‐quality processes, and the time between events (TBE$TBE$) is likely to be followed by a skewed distribution, such as an exponential distribution. This paper proposes the upper and lower‐sided improved adaptive exponentially weighted moving control charts for monitoring TBE$TBE$ data modeled by the exponential distribution. The proposed control charts are labeled as IAEWMATBE$IAEWM{A_{TBE}}$ control charts, that is, the IAEWMATBEU$IAEWMA_{TBE}^U$ and IAEWMATBEL$IAEWMA_{TBE}^L$ control chart, respectively. The IAEWMATBEU$IAEWMA_{TBE}^U$ control chart detects the upward shifts, while the IAEWMATBEL$IAEWMA_{TBE}^L$ control chart identifies the downward shifts in the process. The Monte Carlo simulations are used to approximate the run length distribution of the proposed control charts. Numerical results associated with various performance measures, such as average run length (ARL$ARL$), standard run length (SDRL$SDRL$), median run length (MRL$MRL$), extra quadratic loss (EQL$EQL$), relative average run length (RARL$RARL$), and performance comparison index (PCI$PCI$) are computed. The proposed control charts compared to the respective existing control charts, such as AEWMATBE$AEWM{A_{TBE}}$, IEWMATBE$IEWM{A_{TBE}}$, REWMATBE$REWM{A_{TBE}}$, and ShewhartTBE${\rm{Shewhar}}{{\rm{t}}_{TBE}}$ control charts, at a single shift, as well as over a specified range of shifts. The comparison reveals that the proposed control charts outperform the existing control charts for both single specified shifts and over a certain range of shifts. Finally, real‐life data of hospital stay time for male patients with traumatic brain injury are analyzed for the applicability of the IAEWMATBEU$IAEWMA_{TBE}^U$ control chart in the health sector. [ABSTRACT FROM AUTHOR]

Nonparametric (distribution-free) control charts have been introduced in recent years when quality characteristics do not follow a specific distribution. When the sample selection is prohibitively expensive, we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts. In this study, we proposed a nonparametric homogeneously weighted moving average based on the Wilcoxon signed-rank test with ranked set sampling (NPHWMARSS) control chart for detecting shifts in the process location of a continuous and symmetric distribution. Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart. The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts. These control charts include the exponentially weighted moving average (EWMA) control chart, Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart, the nonparametric EWMA sign control chart, Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart, and the homogeneously weighted moving average control charts. The findings show that the proposed NPHWMARSS control chart performs better than its competitors, particularly for the small shifts. Finally, an example is presented to demonstrate how the proposed scheme can be implemented practically. [ABSTRACT FROM AUTHOR]

The quality characteristic(s) are assumed to follow the normal distribution in many control chart constructions, although this assumption may not hold in some instances. This study proposes the Bayesian-I and Bayesian-II Shewhart-type control charts for monitoring the Maxwell scale parameter in the phase II study. The posterior and predictive distributions are used to construct the control limits for the proposed Bayesian-I and Bayesian-II Shewhart-type control charts, respectively. Various performance indicators, including average run length, quadratic loss, relative average run length, and performance comparison index, are utilized to evaluate the performance of the proposed control charts. The Bayesian-I and Bayesian-II Shewhart-type control charts are compared to their competitive CUSUMV, EWMAV and V control charts. Sensitivity analysis is also performed to study the effect of hyperparameter values on the performance behavior of the proposed control charts. Finally, real-life data is analyzed for the implementation of the proposed control charts. [ABSTRACT FROM AUTHOR]

The recently introduced triple exponentially weighted moving average (TEWMA) chart is the extended form of the classical EWMA and double EWMA (DEWMA) charts. On the other hand, the auxiliary information-based (AIB) homogeneously weighted moving average ( HWMA AIB ) chart is used for the monitoring of process location shifts efficiently as compared to the HWMA chart. Combining TEWMA with HWMA features is a new idea and is not seen in the literature until now. So, the objective of this study is to combine the idea of HWMA AIB and TEWMA charts and propose an AIB triple HWMA, symbolized as THWMA AIB chart to further improve the process location shift monitoring. The proposed THWMA AIB chart is developed by combining the AIB double HWMA plotting statistic into the other HWMA chart. The numerical results are computed using the Monte Carlo simulation method. Average run length (ARL), relative ARL , performance comparison index, and extra quadratic loss are used as comparison tools for the proposed THWMA AIB chart with the classical EWMA, TEWMA, mixed HWMA-CUSUM (MHC), AIB EWMA ( EWMA AIB ), HWMA, double HWMA (DHWMA), HWMA AIB , AIB mixed EWMA-CUSUM ( MEC AIB ), and AIB mixed CUSUM-EWMA ( MCE AIB ) charts. Finally, a practical application is also provided for users to demonstrate the proposed study's vitality. [ABSTRACT FROM AUTHOR]

The basic assumption of the parametric control charts is that the underlying process follows the specific distribution. The appropriateness of parametric control charts is questionable when different industrial applications do not support this desired assumption. Recently, nonparametric control charts have been introduced to overcome this deficiency of parametric control charts. Nonparametric control charts have the same in-control run-length characteristics for all continuous distributions and are in-control robust. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique with control charts because it reduces variability and improves the control chart's performance. So, this study aims to propose a nonparametric triple homogenously weighted moving average control chart under Wilcoxon signed-rank test with a ranked set sampling technique (regarded as NPTHWMA RSS ) to further enhance the process location monitoring. Monte Carlo simulations are used for computational purposes. The proposed control chart's run-length performance is compared with competing control charts, like TEWMA-SR, TEWMA- X ¯ , TEWMA-SN, TEWMA- SR RSS , and NPDHWMA RSS control charts. The comparison revealed that the proposed NPTHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is presented for quality practitioners to illustrate the effectiveness of the proposed control chart. [ABSTRACT FROM AUTHOR]

The adaptive exponentially weighted moving average (AEWMA) control charts are the advanced form of classical memory control charts used for efficiently monitoring small-to-large shifts in the process parameters (location and/or dispersion). These AEWMA control charts estimate the unknown shifts using exponentially weighted moving average (EWMA) or cumulative sum (CUSUM) control charts statistics. The hybrid EWMA (HEWMA) control chart is preferred over classical memory control charts to detect early shifts in process parameters. So, this study presents a new auxiliary information-based (AIB) AEWMA (IAEWMAAIB) control chart for process location that estimates the unknown location shift using HEWMA statistic. The objective is to develop an unbiased location shift estimator using HEWMA statistic and then adaptively update the smoothing constant. The shift estimation using HEWMA statistic instead of EWMA or CUSUM statistics boosts the performance of the proposed IAEWMAAIB control chart. The Monte Carlo simulation technique is used to get the numerical results. Famous performance evaluation measures like average run length, extra quadratic loss, relative average run length, and performance comparison index are used to evaluate the performance of the proposed chart with existing counterparts. The comparison reveals the superiority of the proposed control chart. Finally, two real-life applications from the glass manufacturing industry and physicochemical parameters of groundwater are considered to show the proposed control chart's implementation procedure and dominance. [ABSTRACT FROM AUTHOR]

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart's performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMA RSS ), to further enhance the process location monitoring. The proposed chart's run-length performance is compared with competing control charts, such as DEWMA- X ¯ , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMA RSS control charts. The comparison revealed that the proposed NPDHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart. [ABSTRACT FROM AUTHOR]

The hybrid exponentially weighted moving average (HEWMA) control chart is an enhanced version of the EWMA control chart that monitors the process parameters effectively. Similarly, the auxiliary information-based (AIB) EWMA control charts are very efficient for monitoring process parameters. The purpose of this paper is to propose two new control charts for the improved monitoring of process dispersion referred to as HEWMA AIB 1 and HEWMA AIB 2 control charts. A simulation study is carried out to assess the performance of the proposed HEWMA AIB 1 and HEWMA AIB 2 control charts. Average run length, extra quadratic loss, relative average run length, and performance comparison index are used to compare the performance of the proposed control charts against the existing counterparts. The comparisons reveal the superiority of the proposed control charts against other competing control charts, particularly for small to moderate shifts in the process dispersion. Finally, a real-life data set from the glass industry is used to demonstrate the practical implementation of the proposed control charts. [ABSTRACT FROM AUTHOR]

The EWMA charts are the well-known memory-type charts used for monitoring the small-to-intermediate shifts in the process parameters (location and/or dispersion). The hybrid EWMA (HEWMA) charts are enhanced version of the EWMA charts, which effectively monitor the process parameters. This paper aims to develop two new upper-sided HEWMA charts for monitoring shifts in process variance, i.e., HEWMA1 and HEWMA2 charts. The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMA charts. The HEWMA1 and HEWMA2 charts plotting statistics are developed using one EWMA statistic as input for the other EWMA statistic. A Monte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics, such as average run length (ARL), median run length, and standard deviation run length (SDRL) for assessing the performance of the proposed HEWMA1 and HEWMA2 charts. In addition, to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts, other numerical measures consisting of the extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) are also computed. The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts, such as CH, CEWMA, HEWMA, AEWMA HHW1, HHW2, AIB-EWMA-I, and AIB-EWMA-II charts, on the basis aforementioned numerical measures. The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts. In the end, a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically. [ABSTRACT FROM AUTHOR]

In high‐quality processes, non‐conforming events rarely occur, and the time between events (TBE) is more likely to follow a skewed distribution, such as gamma distribution. This paper proposes a gamma distribution‐based one‐sided homogeneously weighted moving average control chart for monitoring the TBE. The proposed control chart is known as the HWMA_TBE control chart. The HWMA_TBE control chart monitors the downward shifts in the process, that is, a decrease in inter‐arrival time that can lead to the process deterioration. The Monte Carlo simulation approach is used to compute specific performance indicators, such as average run length (ARL${\rm{ARL}}$), standard deviation run length (SDRL)$({{\rm{SDRL}}})$, extra quadratic loss (EQL${\rm{EQL}}$), relative average run length (RARL${\rm{RARL}}$), and performance comparison index (PCI${\rm{PCI}}$). Based on these performance indicators, the HWMA_TBE control chart is compared to some competing control charts. The comparison suggests that the HWMA_TBE control chart is more efficient than the competing control charts. Moreover, this paper also investigates the robustness of the HWMA_TBE control chart, which indicates that the HWMA_TBE control chart is more robust than the competing control charts. In the end, two examples are provided, one with boring machine failure data and the other with breast cancer survival data, to evaluate the implementation of the HWMA_TBE control chart for practical situations. [ABSTRACT FROM AUTHOR]